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Order-Isomorphic Twins in Permutations
SIAM Journal on Discrete Mathematics ( IF 0.9 ) Pub Date : 2020-07-27 , DOI: 10.1137/20m1323357 Boris Bukh , Oleksandr Rudenko
SIAM Journal on Discrete Mathematics ( IF 0.9 ) Pub Date : 2020-07-27 , DOI: 10.1137/20m1323357 Boris Bukh , Oleksandr Rudenko
SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1620-1622, January 2020.
Let $a_1,\ldots,a_n$ be a permutation of $[n]$. Two disjoint order-isomorphic subsequences are called twins. We show that every permutation of $[n]$ contains twins of length $\Omega(n^{3/5})$ improving the trivial bound of $\Omega(n^{1/2})$. We also show that a random permutation contains twins of length $\Omega(n^{2/3})$, which is sharp.
中文翻译:
排列中的同构同卵双胞胎
SIAM离散数学杂志,第34卷,第3期,第1620-1622页,2020年1月。
令$ a_1,\ ldots,a_n $为$ [n] $的排列。两个不相交的阶同构子序列称为孪生子。我们显示$ [n] $的每个排列都包含长度为\\ Omega(n ^ {3/5})$的双胞胎,从而改善了$ \ Omega(n ^ {1/2})$的琐碎界限。我们还显示,随机排列包含长度为\\ Omega(n ^ {2/3})$的双胞胎,这很明显。
更新日期:2020-07-27
Let $a_1,\ldots,a_n$ be a permutation of $[n]$. Two disjoint order-isomorphic subsequences are called twins. We show that every permutation of $[n]$ contains twins of length $\Omega(n^{3/5})$ improving the trivial bound of $\Omega(n^{1/2})$. We also show that a random permutation contains twins of length $\Omega(n^{2/3})$, which is sharp.
中文翻译:
排列中的同构同卵双胞胎
SIAM离散数学杂志,第34卷,第3期,第1620-1622页,2020年1月。
令$ a_1,\ ldots,a_n $为$ [n] $的排列。两个不相交的阶同构子序列称为孪生子。我们显示$ [n] $的每个排列都包含长度为\\ Omega(n ^ {3/5})$的双胞胎,从而改善了$ \ Omega(n ^ {1/2})$的琐碎界限。我们还显示,随机排列包含长度为\\ Omega(n ^ {2/3})$的双胞胎,这很明显。